Question: Solve for $x$ and $y$ using elimination. ${-x-5y = -33}$ ${-x-4y = -27}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-x-5y = -33}$ $x+4y = 27$ Add the top and bottom equations together. $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-x-5y = -33}\thinspace$ to find $x$ ${-x - 5}{(6)}{= -33}$ $-x-30 = -33$ $-x-30{+30} = -33{+30}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 6}$ into $\thinspace {-x-4y = -27}\thinspace$ and get the same answer for $x$ : ${-x - 4}{(6)}{= -27}$ ${x = 3}$